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**[SOLVED] Vector Problem**

I hope someone can help me. I am so tired of trying to figure this out.

**A man pushing a mop across a floor causes the map to undergo two displacements. The first has a magnitude of 110 cm and makes an angle of 110° with the positive x axis. The resultant displacement has a magnitude of 240 cm and is directed at an angle of 25.0° to the positive x axis. Find the magnitude and direction of the second displacement. Find the angle with respect to the positive x axis.**

I started by measuring 110 degrees and drew my vector starting at the origin (origin is point A). The end of this first vector is point C. Then, starting at point A again (since this vector is the resultant vector) I measured an angle of 155 degrees (180-25=155) and drew my vector, the end of which is labeled point B. I then drew the connecting vector, vector BC.

Now, I drew a line straight down from point B to the x-axis. This point is D. I need to find the x and y components of this right triangle, triangle ABD. By using the angle of 155 degrees I can say cos155=x divided by 240. This equals -217.5139. To find y, I can say sin155=y divided by 240. This is 101.4284.

Now, I drew a line from point C straight over to the y-axis. This will be point E. I need to find the components of triangle ACE. So, cos110=x divided by 110. This is -37.6222. And sin110=y divided by 110. This is 103.3662.

This is the point where I'm not sure what to do. Since the unknown vector, BC, is a hypotenuse of a third right triangle, I just don't know what to do next. I thought I could take the difference of the x values and y values I found, then use the Pythagorean theorem to get vector BC, but I get the wrong answer. (I keep getting vector BC equals 180.)

I hope I was able to explain what I did without confusing anyone. I would be ever so grateful for some help.